You are moving the goalposts again and again, which is why I asked you for the criteria necessary to change your viewpoint. It's clear that you won't, and this will be an endless and fruitless exchange. However, Duty Calls[0].

> You've given examples of old theorems, and also said
> they weren't actually useful at first.

We don't know what of today's work will become useful, or how. I can only give you hindsight evidence, because prediction is hard, especially of the future[1].

> Later practical work lead to someone seeing use in them
> (but only the a vague way - limits - which could have
> been and probably found through experiment as well).

It's limits that are especially hard to establish with experimentation. How do you know that you just haven't yet been clever enough? How do you know that this will always work no matter how far you go? Remember the Ariane 5 explosion? The maiden flight of the Ariane 5 rocket, Flight 501, was lost because engineers reused a unit that had worked flawlessly in every previous flight. The limits were not well understood, and experimentation was expensive. These are guiding principles - sometimes understanding the theory helps more than twiddling bits and seeing what happens. Sometimes twiddling bits is enough. Engineering and Theoretical Research should work together.

In my own work there are at least a dozen cases where knowing a theorem has provoked an exploration, that has then turned out to be useful. The investigation would most likely never have started, the techniques never suspected, without that initial theoretical knowledge. Again, engineering and pure math research in combination, but without the pure math to start with, some things might never be found. We can't know that, of course, but for those who have studied math, the connection is clear. For those who haven't, it's harder to see these things happen. It all seems so obvious in retrospect.

> The example you gave of your proof doesn't say all
> that much, you won an argument (you said those
> algorithms were practically useful anyway).

So, you don't get the idea then. I proved something was impossible given our current state of theoretical knowledge, and that if the claims were correct it was an outstanding breakthrough. He proved nothing, and had a system that worked sometimes, and he was unable to know when, and how, it might fail. I predicted - using pure math research - exactly how his system would fail. I could do something he couldn't, using his system that he created.

> I'm sincerely sorry if I come across as hostile.

Hmm. let's see some of the things you've said:

> ... rarefied "breed" of pure mathematician earning a
> salary is as much of a waste as if billions were spent
> on buggy whip boys.

... and ...

> ... it's the full employment act for pencil pushers.

... and ...

> A lot in common with fundamental religionists.

... and ...

> I never tried getting education in it in the first place.
> I had hunch it's useless and the older I get the more
> I think that was correct.

... and ...

> It's justification for pencil pushers who don't want
> to do real work.

Yes, that does seem hostile. In fact, it seems like you never bothered to study math, and now are trying to convince everyone that something you don't understand cannot possibly be useful.

> I'd just like to see mathematicians own up and change
> the corruption from the inside.

Hmm.

> ... you've taken up a lot it's (sic) resources, including
> some of the smartest people.

So some of the smartest people study math and claim that it is a good thing to be doing. You, on the other hand, claim that it isn't. Your position seems difficult. You claim that something you've not studied, and which is studied and commended by some of the world's smartest people (by your own claim) is, in fact, useless.

Again, I'll never convince you, but I thought your comments should not stand without reply. Perhaps you are in earnest and genuinely believe the things you say, but you are arguing from a position of willful ignorance, which makes it hard to take you seriously.

[0] http://xkcd.com/386/

[1] "Prediction is very difficult, especially about the future." -- Niels Bohr